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rational_interpolant_greedy_pivoted.py
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R6746 RationalROMPy
rational_interpolant_greedy_pivoted.py
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# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see <http://www.gnu.org/licenses/>.
#
from
copy
import
deepcopy
as
copy
import
numpy
as
np
from
.generic_pivoted_approximant
import
(
GenericPivotedApproximantBase
,
GenericPivotedApproximantNoMatch
,
GenericPivotedApproximant
)
from
.gather_pivoted_approximant
import
gatherPivotedApproximant
from
rrompy.reduction_methods.standard.greedy.rational_interpolant_greedy
\
import
RationalInterpolantGreedy
from
rrompy.reduction_methods.standard.greedy.generic_greedy_approximant
\
import
pruneSamples
from
rrompy.utilities.base.types
import
Np1D
from
rrompy.utilities.base
import
verbosityManager
as
vbMng
from
rrompy.utilities.poly_fitting.polynomial
import
polyvander
as
pv
from
rrompy.utilities.exception_manager
import
RROMPyAssert
from
rrompy.parameter
import
emptyParameterList
,
parameterList
from
rrompy.utilities.parallel
import
poolRank
,
indicesScatter
,
isend
,
recv
__all__
=
[
'RationalInterpolantGreedyPivotedNoMatch'
,
'RationalInterpolantGreedyPivoted'
]
class
RationalInterpolantGreedyPivotedBase
(
GenericPivotedApproximantBase
,
RationalInterpolantGreedy
):
def
__init__
(
self
,
*
args
,
**
kwargs
):
self
.
_preInit
()
super
()
.
__init__
(
*
args
,
**
kwargs
)
self
.
_ignoreResidues
=
self
.
nparPivot
>
1
self
.
_postInit
()
@property
def
tModelType
(
self
):
if
hasattr
(
self
,
"_temporaryPivot"
):
return
RationalInterpolantGreedy
.
tModelType
.
fget
(
self
)
return
super
()
.
tModelType
def
_polyvanderAuxiliary
(
self
,
mus
,
deg
,
*
args
):
degEff
=
[
0
]
*
self
.
npar
degEff
[
self
.
directionPivot
[
0
]]
=
deg
return
pv
(
mus
,
degEff
,
*
args
)
def
_marginalizeMiscellanea
(
self
,
forward
:
bool
):
if
forward
:
self
.
_m_selfmus
=
copy
(
self
.
mus
)
self
.
_m_HFEparameterMap
=
copy
(
self
.
HFEngine
.
parameterMap
)
self
.
_mus
=
self
.
checkParameterListPivot
(
self
.
mus
(
self
.
directionPivot
))
self
.
HFEngine
.
parameterMap
=
{
"F"
:
[
self
.
HFEngine
.
parameterMap
[
"F"
][
self
.
directionPivot
[
0
]]],
"B"
:
[
self
.
HFEngine
.
parameterMap
[
"B"
][
self
.
directionPivot
[
0
]]]}
else
:
self
.
_mus
=
self
.
_m_selfmus
self
.
HFEngine
.
parameterMap
=
self
.
_m_HFEparameterMap
del
self
.
_m_selfmus
,
self
.
_m_HFEparameterMap
def
_marginalizeTrainedModel
(
self
,
forward
:
bool
):
if
forward
:
del
self
.
_temporaryPivot
self
.
trainedModel
.
data
.
mu0
=
self
.
mu0
self
.
trainedModel
.
data
.
scaleFactor
=
[
1.
]
*
self
.
npar
self
.
trainedModel
.
data
.
scaleFactor
[
self
.
directionPivot
[
0
]]
=
(
self
.
scaleFactor
[
0
])
self
.
trainedModel
.
data
.
parameterMap
=
self
.
HFEngine
.
parameterMap
self
.
_m_musUniqueCN
=
copy
(
self
.
_musUniqueCN
)
musUniqueCNAux
=
np
.
zeros
((
self
.
S
,
self
.
npar
),
dtype
=
self
.
_musUniqueCN
.
dtype
)
musUniqueCNAux
[:,
self
.
directionPivot
[
0
]]
=
self
.
_musUniqueCN
(
0
)
self
.
_musUniqueCN
=
self
.
checkParameterList
(
musUniqueCNAux
)
self
.
_m_derIdxs
=
copy
(
self
.
_derIdxs
)
for
j
in
range
(
len
(
self
.
_derIdxs
)):
for
l
in
range
(
len
(
self
.
_derIdxs
[
j
])):
derjl
=
self
.
_derIdxs
[
j
][
l
][
0
]
self
.
_derIdxs
[
j
][
l
]
=
[
0
]
*
self
.
npar
self
.
_derIdxs
[
j
][
l
][
self
.
directionPivot
[
0
]]
=
derjl
self
.
trainedModel
.
data
.
Q
.
_dirPivot
=
self
.
directionPivot
[
0
]
self
.
trainedModel
.
data
.
P
.
_dirPivot
=
self
.
directionPivot
[
0
]
else
:
self
.
_temporaryPivot
=
1
self
.
trainedModel
.
data
.
mu0
=
self
.
checkParameterListPivot
(
self
.
mu0
(
self
.
directionPivot
))
self
.
trainedModel
.
data
.
scaleFactor
=
self
.
scaleFactor
self
.
trainedModel
.
data
.
parameterMap
=
{
"F"
:
[
self
.
HFEngine
.
parameterMap
[
"F"
][
self
.
directionPivot
[
0
]]],
"B"
:
[
self
.
HFEngine
.
parameterMap
[
"B"
][
self
.
directionPivot
[
0
]]]}
self
.
_musUniqueCN
=
copy
(
self
.
_m_musUniqueCN
)
self
.
_derIdxs
=
copy
(
self
.
_m_derIdxs
)
del
self
.
_m_musUniqueCN
,
self
.
_m_derIdxs
del
self
.
trainedModel
.
data
.
Q
.
_dirPivot
del
self
.
trainedModel
.
data
.
P
.
_dirPivot
self
.
trainedModel
.
data
.
npar
=
self
.
npar
def
errorEstimator
(
self
,
mus
:
Np1D
,
return_max
:
bool
=
False
)
->
Np1D
:
"""Standard residual-based error estimator."""
self
.
_marginalizeMiscellanea
(
True
)
setupOK
=
self
.
setupApproxLocal
()
self
.
_marginalizeMiscellanea
(
False
)
if
setupOK
>
0
:
err
=
np
.
empty
(
len
(
mus
))
err
[:]
=
np
.
nan
if
not
return_max
:
return
err
return
err
,
[
-
setupOK
],
np
.
nan
self
.
_marginalizeTrainedModel
(
True
)
errRes
=
super
()
.
errorEstimator
(
mus
,
return_max
)
self
.
_marginalizeTrainedModel
(
False
)
return
errRes
def
_preliminaryTraining
(
self
):
"""Initialize starting snapshots of solution map."""
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot start greedy algorithm."
)
self
.
_S
=
self
.
_setSampleBatch
(
self
.
S
)
self
.
resetSamples
()
self
.
samplingEngine
.
scaleFactor
=
self
.
scaleFactorDer
musPivot
=
self
.
trainSetGenerator
.
generatePoints
(
self
.
S
)
while
len
(
musPivot
)
>
self
.
S
:
musPivot
.
pop
()
muTestPivot
=
self
.
samplerPivot
.
generatePoints
(
self
.
nTestPoints
,
False
)
idxPop
=
pruneSamples
(
self
.
mapParameterListPivot
(
muTestPivot
),
self
.
mapParameterListPivot
(
musPivot
),
1e-10
*
self
.
scaleFactorPivot
[
0
])
self
.
_mus
=
emptyParameterList
()
self
.
mus
.
reset
((
self
.
S
,
self
.
npar
+
len
(
self
.
musMargLoc
)))
muTestBase
=
emptyParameterList
()
muTestBase
.
reset
((
len
(
muTestPivot
),
self
.
npar
+
len
(
self
.
musMargLoc
)))
for
k
in
range
(
self
.
S
):
muk
=
np
.
empty_like
(
self
.
mus
[
0
])
muk
[
self
.
directionPivot
]
=
musPivot
[
k
]
muk
[
self
.
directionMarginal
]
=
self
.
musMargLoc
self
.
mus
[
k
]
=
muk
for
k
in
range
(
len
(
muTestPivot
)):
muk
=
np
.
empty_like
(
muTestBase
[
0
])
muk
[
self
.
directionPivot
]
=
muTestPivot
[
k
]
muk
[
self
.
directionMarginal
]
=
self
.
musMargLoc
muTestBase
[
k
]
=
muk
muTestBase
.
pop
(
idxPop
)
muLast
=
copy
(
self
.
mus
[
-
1
])
self
.
mus
.
pop
()
if
len
(
self
.
mus
)
>
0
:
vbMng
(
self
,
"MAIN"
,
(
"Adding first {} sample point{} at {} to training "
"set."
)
.
format
(
self
.
S
-
1
,
""
+
"s"
*
(
self
.
S
>
2
),
self
.
mus
),
3
)
self
.
samplingEngine
.
iterSample
(
self
.
mus
)
self
.
_S
=
len
(
self
.
mus
)
self
.
_approxParameters
[
"S"
]
=
self
.
S
self
.
muTest
=
parameterList
(
muTestBase
)
self
.
muTest
.
append
(
muLast
)
self
.
M
,
self
.
N
=
(
"AUTO"
,)
*
2
def
setupApprox
(
self
,
*
args
,
**
kwargs
)
->
int
:
"""Compute rational interpolant."""
if
self
.
checkComputedApprox
():
return
-
1
RROMPyAssert
(
self
.
_mode
,
message
=
"Cannot setup approximant."
)
vbMng
(
self
,
"INIT"
,
"Setting up {}."
.
format
(
self
.
name
()),
5
)
self
.
computeScaleFactor
()
self
.
_musMarginal
=
self
.
samplerMarginal
.
generatePoints
(
self
.
SMarginal
)
while
len
(
self
.
musMarginal
)
>
self
.
SMarginal
:
self
.
musMarginal
.
pop
()
S0
=
copy
(
self
.
S
)
idx
,
sizes
=
indicesScatter
(
len
(
self
.
musMarginal
),
return_sizes
=
True
)
pMat
,
Ps
,
Qs
,
mus
=
None
,
[],
[],
None
req
,
emptyCores
=
[],
np
.
where
(
np
.
logical_not
(
sizes
))[
0
]
if
len
(
idx
)
==
0
:
vbMng
(
self
,
"MAIN"
,
"Idling."
,
25
)
if
self
.
storeAllSamples
:
self
.
storeSamples
()
pL
,
pT
,
mT
=
recv
(
source
=
0
,
tag
=
poolRank
())
pMat
=
np
.
empty
((
pL
,
0
),
dtype
=
pT
)
mus
=
np
.
empty
((
0
,
self
.
mu0
.
shape
[
1
]),
dtype
=
mT
)
else
:
_scaleFactorOldPivot
=
copy
(
self
.
scaleFactor
)
self
.
scaleFactor
=
self
.
scaleFactorPivot
self
.
_temporaryPivot
=
1
for
i
in
idx
:
self
.
musMargLoc
=
self
.
musMarginal
[
i
]
vbMng
(
self
,
"MAIN"
,
"Building marginal model no. {} at {}."
.
format
(
i
+
1
,
self
.
musMargLoc
),
5
)
self
.
samplingEngine
.
resetHistory
()
self
.
trainedModel
=
None
self
.
verbosity
-=
5
self
.
samplingEngine
.
verbosity
-=
5
super
()
.
setupApprox
(
*
args
,
**
kwargs
)
self
.
verbosity
+=
5
self
.
samplingEngine
.
verbosity
+=
5
if
self
.
storeAllSamples
:
self
.
storeSamples
(
i
)
if
pMat
is
None
:
mus
=
copy
(
self
.
samplingEngine
.
mus
.
data
)
pMat
=
copy
(
self
.
samplingEngine
.
projectionMatrix
)
if
i
==
0
:
for
dest
in
emptyCores
:
req
+=
[
isend
((
len
(
pMat
),
pMat
.
dtype
,
mus
.
dtype
),
dest
=
dest
,
tag
=
dest
)]
else
:
mus
=
np
.
vstack
((
mus
,
self
.
samplingEngine
.
mus
.
data
))
pMat
=
np
.
hstack
((
pMat
,
self
.
samplingEngine
.
projectionMatrix
))
Ps
+=
[
copy
(
self
.
trainedModel
.
data
.
P
)]
Qs
+=
[
copy
(
self
.
trainedModel
.
data
.
Q
)]
self
.
_S
=
S0
del
self
.
_temporaryPivot
,
self
.
musMargLoc
self
.
scaleFactor
=
_scaleFactorOldPivot
for
r
in
req
:
r
.
wait
()
pMat
,
Ps
,
Qs
,
mus
,
nsamples
=
gatherPivotedApproximant
(
pMat
,
Ps
,
Qs
,
mus
,
sizes
,
self
.
polybasis
)
self
.
_mus
=
self
.
checkParameterList
(
mus
)
Psupp
=
np
.
append
(
0
,
np
.
cumsum
(
nsamples
))
self
.
_setupTrainedModel
(
pMat
,
forceNew
=
True
)
self
.
trainedModel
.
data
.
Qs
,
self
.
trainedModel
.
data
.
Ps
=
Qs
,
Ps
self
.
trainedModel
.
data
.
Psupp
=
list
(
Psupp
[:
-
1
])
self
.
_poleMatching
()
self
.
_finalizeMarginalization
()
vbMng
(
self
,
"DEL"
,
"Done setting up approximant."
,
5
)
return
0
class
RationalInterpolantGreedyPivotedNoMatch
(
RationalInterpolantGreedyPivotedBase
,
GenericPivotedApproximantNoMatch
):
"""
ROM pivoted rational interpolant (without pole matching) computation for
parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
directionPivot(optional): Pivot components. Defaults to [0].
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'scaleFactorDer': scaling factors for derivative computation;
defaults to 'AUTO';
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator;
- 'polybasis': type of polynomial basis for pivot
interpolation; defaults to 'MONOMIAL';
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
defaults to 0.;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'nTestPoints': number of test points; defaults to 5e2;
- 'trainSetGenerator': training sample points generator; defaults
to sampler;
- 'errorEstimatorKind': kind of error estimator; available values
include 'AFFINE', 'DISCREPANCY', 'LOOK_AHEAD',
'LOOK_AHEAD_RES', and 'NONE'; defaults to 'NONE';
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'functionalSolve': strategy for minimization of denominator
functional; allowed values include 'NORM', 'DOMINANT', 'NODAL',
'LOEWNER', and 'BARYCENTRIC'; defaults to 'NORM';
- 'interpRcond': tolerance for pivot interpolation; defaults to
None;
- 'robustTol': tolerance for robust rational denominator
management; defaults to 0.
Defaults to empty dict.
approx_state(optional): Whether to approximate state. Defaults to
False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
directionPivot: Pivot components.
mus: Array of snapshot parameters.
musMarginal: Array of marginal snapshot parameters.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'scaleFactorDer': scaling factors for derivative computation;
- 'polybasis': type of polynomial basis for pivot
interpolation;
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
- 'maxIter': maximum number of greedy steps;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator;
- 'errorEstimatorKind': kind of error estimator;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'functionalSolve': strategy for minimization of denominator
functional;
- 'interpRcond': tolerance for pivot interpolation;
- 'robustTol': tolerance for robust rational denominator
management.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator.
approx_state: Whether to approximate state.
verbosity: Verbosity level.
POD: Whether to compute POD of snapshots.
scaleFactorDer: Scaling factors for derivative computation.
S: Total number of pivot samples current approximant relies upon.
samplerPivot: Pivot sample point generator.
SMarginal: Total number of marginal samples current approximant relies
upon.
samplerMarginal: Marginal sample point generator.
polybasis: Type of polynomial basis for pivot interpolation.
greedyTol: uniform error tolerance for greedy algorithm.
collinearityTol: Collinearity tolerance for greedy algorithm.
maxIter: maximum number of greedy steps.
nTestPoints: number of starting training points.
trainSetGenerator: training sample points generator.
errorEstimatorKind: kind of error estimator.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
functionalSolve: Strategy for minimization of denominator functional.
interpRcond: Tolerance for pivot interpolation.
robustTol: Tolerance for robust rational denominator management.
muBounds: list of bounds for pivot parameter values.
muBoundsMarginal: list of bounds for marginal parameter values.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
Q: Numpy 1D vector containing complex coefficients of approximant
denominator.
P: Numpy 2D vector whose columns are FE dofs of coefficients of
approximant numerator.
"""
class
RationalInterpolantGreedyPivoted
(
RationalInterpolantGreedyPivotedBase
,
GenericPivotedApproximant
):
"""
ROM pivoted rational interpolant (with pole matching) computation for
parametric problems.
Args:
HFEngine: HF problem solver.
mu0(optional): Default parameter. Defaults to 0.
directionPivot(optional): Pivot components. Defaults to [0].
approxParameters(optional): Dictionary containing values for main
parameters of approximant. Recognized keys are:
- 'POD': whether to compute POD of snapshots; defaults to True;
- 'scaleFactorDer': scaling factors for derivative computation;
defaults to 'AUTO';
- 'matchingWeight': weight for pole matching optimization; defaults
to 1;
- 'matchingMode': mode for pole matching optimization; allowed
values include 'NONE' and 'SHIFT'; defaults to 'NONE';
- 'sharedRatio': required ratio of marginal points to share
resonance; defaults to 1.;
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator;
- 'polybasis': type of polynomial basis for pivot
interpolation; defaults to 'MONOMIAL';
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation; allowed values include 'MONOMIAL_*',
'CHEBYSHEV_*', 'LEGENDRE_*', 'NEARESTNEIGHBOR', and
'PIECEWISE_LINEAR_*'; defaults to 'MONOMIAL';
- 'paramsMarginal': dictionary of parameters for marginal
interpolation; include:
. 'MMarginal': degree of marginal interpolant; defaults to
'AUTO', i.e. maximum allowed; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'nNeighborsMarginal': number of marginal nearest neighbors;
defaults to 1; only for 'NEARESTNEIGHBOR';
. 'polydegreetypeMarginal': type of polynomial degree for
marginal; defaults to 'TOTAL'; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'interpRcondMarginal': tolerance for marginal interpolation;
defaults to None; not for 'NEARESTNEIGHBOR' or
'PIECEWISE_LINEAR_*';
. 'radialDirectionalWeightsMarginalAdapt': bounds for adaptive
rescaling of marginal radial basis weights; only for
radial basis.
- 'greedyTol': uniform error tolerance for greedy algorithm;
defaults to 1e-2;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
defaults to 0.;
- 'maxIter': maximum number of greedy steps; defaults to 1e2;
- 'nTestPoints': number of test points; defaults to 5e2;
- 'trainSetGenerator': training sample points generator; defaults
to sampler;
- 'errorEstimatorKind': kind of error estimator; available values
include 'AFFINE', 'DISCREPANCY', 'LOOK_AHEAD',
'LOOK_AHEAD_RES', and 'NONE'; defaults to 'NONE';
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant; defaults to 1;
- 'functionalSolve': strategy for minimization of denominator
functional; allowed values include 'NORM', 'DOMINANT', 'NODAL',
'LOEWNER', and 'BARYCENTRIC'; defaults to 'NORM';
- 'interpRcond': tolerance for pivot interpolation; defaults to
None;
- 'robustTol': tolerance for robust rational denominator
management; defaults to 0.
Defaults to empty dict.
approx_state(optional): Whether to approximate state. Defaults to
False.
verbosity(optional): Verbosity level. Defaults to 10.
Attributes:
HFEngine: HF problem solver.
mu0: Default parameter.
directionPivot: Pivot components.
mus: Array of snapshot parameters.
musMarginal: Array of marginal snapshot parameters.
approxParameters: Dictionary containing values for main parameters of
approximant. Recognized keys are in parameterList.
parameterListSoft: Recognized keys of soft approximant parameters:
- 'POD': whether to compute POD of snapshots;
- 'scaleFactorDer': scaling factors for derivative computation;
- 'matchingWeight': weight for pole matching optimization;
- 'matchingMode': mode for pole matching optimization;
- 'sharedRatio': required ratio of marginal points to share
resonance;
- 'polybasis': type of polynomial basis for pivot
interpolation;
- 'polybasisMarginal': type of polynomial basis for marginal
interpolation;
- 'paramsMarginal': dictionary of parameters for marginal
interpolation; include:
. 'MMarginal': degree of marginal interpolant;
. 'nNeighborsMarginal': number of marginal nearest neighbors;
. 'polydegreetypeMarginal': type of polynomial degree for
marginal;
. 'interpRcondMarginal': tolerance for marginal interpolation;
. 'radialDirectionalWeightsMarginalAdapt': bounds for adaptive
rescaling of marginal radial basis weights.
- 'greedyTol': uniform error tolerance for greedy algorithm;
- 'collinearityTol': collinearity tolerance for greedy algorithm;
- 'maxIter': maximum number of greedy steps;
- 'nTestPoints': number of test points;
- 'trainSetGenerator': training sample points generator;
- 'errorEstimatorKind': kind of error estimator;
- 'radialDirectionalWeightsMarginal': radial basis weights for
marginal interpolant;
- 'functionalSolve': strategy for minimization of denominator
functional;
- 'interpRcond': tolerance for pivot interpolation;
- 'robustTol': tolerance for robust rational denominator
management.
parameterListCritical: Recognized keys of critical approximant
parameters:
- 'S': total number of pivot samples current approximant relies
upon;
- 'samplerPivot': pivot sample point generator;
- 'SMarginal': total number of marginal samples current approximant
relies upon;
- 'samplerMarginal': marginal sample point generator.
approx_state: Whether to approximate state.
verbosity: Verbosity level.
POD: Whether to compute POD of snapshots.
scaleFactorDer: Scaling factors for derivative computation.
matchingWeight: Weight for pole matching optimization.
matchingMode: Mode for pole matching optimization.
sharedRatio: Required ratio of marginal points to share resonance.
S: Total number of pivot samples current approximant relies upon.
samplerPivot: Pivot sample point generator.
SMarginal: Total number of marginal samples current approximant relies
upon.
samplerMarginal: Marginal sample point generator.
polybasis: Type of polynomial basis for pivot interpolation.
polybasisMarginal: Type of polynomial basis for marginal interpolation.
paramsMarginal: Dictionary of parameters for marginal interpolation.
greedyTol: uniform error tolerance for greedy algorithm.
collinearityTol: Collinearity tolerance for greedy algorithm.
maxIter: maximum number of greedy steps.
nTestPoints: number of starting training points.
trainSetGenerator: training sample points generator.
errorEstimatorKind: kind of error estimator.
radialDirectionalWeightsMarginal: Radial basis weights for marginal
interpolant.
functionalSolve: Strategy for minimization of denominator functional.
interpRcond: Tolerance for pivot interpolation.
robustTol: Tolerance for robust rational denominator management.
muBounds: list of bounds for pivot parameter values.
muBoundsMarginal: list of bounds for marginal parameter values.
samplingEngine: Sampling engine.
uHF: High fidelity solution(s) with parameter(s) lastSolvedHF as
sampleList.
lastSolvedHF: Parameter(s) corresponding to last computed high fidelity
solution(s) as parameterList.
uApproxReduced: Reduced approximate solution(s) with parameter(s)
lastSolvedApprox as sampleList.
lastSolvedApproxReduced: Parameter(s) corresponding to last computed
reduced approximate solution(s) as parameterList.
uApprox: Approximate solution(s) with parameter(s) lastSolvedApprox as
sampleList.
lastSolvedApprox: Parameter(s) corresponding to last computed
approximate solution(s) as parameterList.
Q: Numpy 1D vector containing complex coefficients of approximant
denominator.
P: Numpy 2D vector whose columns are FE dofs of coefficients of
approximant numerator.
"""
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